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3 years ago

8

Camilla borrows a book from the library for ddd days. The library charges a late fee of 0.100.100, point, 10 dollars per day tha

t the book is late.
If Camilla returns the book more than 212121 days after she borrowed it, the expression 0.10(d-21)0.10(d−21)0, point, 10, left parenthesis, d, minus, 21, right parenthesis represents the total late fee Camilla owes.

What does (d-21)(d−21)left parenthesis, d, minus, 21, right parenthesis represent in this context?

2 answers:

bixtya [17]3 years ago

4 0

Answer:

(d -21) is the number of days the book is late

Step-by-step explanation:

larisa [96]3 years ago

3 0

Answer:

(d -21) is the number of days the book is late

Step-by-step explanation:

There is no fee if the book is returned within 21 days, so d-21 represents the number of "late days" for which a fee is charged.

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Do my brothers homework I’ll mark you as brainliest

worty [1.4K]

Answer:

can you just snap me the questions

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2 years ago

Consider the differential equation y'' − y' − 20y = 0. Verify that the functions e−4x and e5x form a fundamental set of solution

KIM [24]

Answer:

Therefore $e^{-4x}$ and $e^{5x}$ are fundamental solution of the given differential equation.

Therefore $e^{-4x}$ and $e^{5x}$ are linearly independent, since $W(e^{-4x},e^{5x})=9e^x\neq 0$

The general solution of the differential equation is

$y=c_1e^{-4x}+c_2e^{5x}$

Step-by-step explanation:

Given differential equation is

y''-y'-20y =0

Here P(x)= -1, Q(x)= -20 and R(x)=0

Let trial solution be $y=e^{mx}$

Then, $y'=me^{mx}$ and $y''=m^2e^{mx}$

$\therefore m^2e^{mx}-m e^{mx}-20e^{mx}=0$

$\Rightarrow m^2-m-20=0$

$\Rightarrow m^2-5m+4m-20=0$

$\Rightarrow m(m-5)+4(m-5)=0$

$\Rightarrow (m-5)(m+4)=0$

$\Rightarrow m=-4,5$

Therefore the complementary function is = $c_1e^{-4x}+c_2e^{5x}$

Therefore $e^{-4x}$ and $e^{5x}$ are fundamental solution of the given differential equation.

If $y_1$ and $y_2$ are the fundamental solution of differential equation, then

$W(y_1,y_2)=\left|\begin{array}{cc}y_1&y_2\\y'_1&y'_2\end{array}\right|\neq 0$

Then $y_1$ and $y_2$ are linearly independent.

$W(e^{-4x},e^{5x})=\left|\begin{array}{cc}e^{-4x}&e^{5x}\\-4e^{-4x}&5e^{5x}\end{array}\right|$

$=e^{-4x}.5e^{5x}-e^{5x}.(-4e^{-4x})$

$=5e^x+4e^x$

$=9e^x\neq 0$

Therefore $e^{-4x}$ and $e^{5x}$ are linearly independent, since $W(e^{-4x},e^{5x})=9e^x\neq 0$

Let the the particular solution of the differential equation is

$y_p=v_1e^{-4x}+v_2e^{5x}$

$\therefore v_1=\int \frac{-y_2R(x)}{W(y_1,y_2)} dx$

and

$\therefore v_2=\int \frac{y_1R(x)}{W(y_1,y_2)} dx$

Here $y_1= e^{-4x}$ , $y_2=e^{5x}$ , $W(e^{-4x},e^{5x})=9e^x$ ,and $R(x)=0$

$\therefore v_1=\int \frac{-e^{5x}.0}{9e^x}dx$

=0

and

$\therefore v_2=\int \frac{e^{5x}.0}{9e^x}dx$

=0

The the P.I = 0

The general solution of the differential equation is

$y=c_1e^{-4x}+c_2e^{5x}$

7 0

3 years ago

When 23 mL of water for injection is added to a drug-lyophilized powder, the resulting concentration is 200,000 units per mL. Wh

givi [52]

Answer:

2 mL

Step-by-step explanation:

Given:

Volume of water for injection = 23 mL

Resulting concentration = 200,000 units per mL

Amount of drug in the vial = 5,000,000 units

Now,

Let the final volume of the solution be 'x' mL

Now, concentration = $\frac{\textup{units of the powder}}{\textup{Total volume of the soltuion}}$

thus,

200,000 = $\frac{\textup{5,000,000}}{\textup{x}}$

or

x = 25 mL

also,

Total volume 'x' = volume of water + volume of powder

or

25 mL = 23 + volume of powder

or

Volume of powder = 2 mL

4 0

2 years ago

BRAINLIESTTTTTTTTT! Urgent help needed! Please find the measure of angle B!

Crank

Answer: 59 degrees

--------------------------------------------------------------
--------------------------------------------------------------

Work Shown:

We have the three angles:
angle A = (3x+2) degrees
angle B = (2x+7) degrees
angle C = 41 degrees

Rule: for any triangle, the three angles add up to 180 degrees

(angle A) + (angle B) + (angle C) = 180
(3x+2) + (2x+7) + (41) = 180
3x+2 + 2x+7 + 41 = 180
(3x+2x)+(2+7+41) = 180
(5x)+(50) = 180
5x+50 = 180
5x+50-50 = 180-50
5x = 130
5x/5 = 130/5
x = 26

Now use this x value to find the measure of angle B
angle B = (2x+7) degrees
angle B = (2*x+7) degrees
angle B = (2*26+7) degrees
angle B = (52+7) degrees
angle B = 59 degrees

Side Note: Angle A is 80 degrees (3x+2 = 3*26+2 = 78+2 = 80)

Another thing to note: A+B+C = 80+59+41 = 180

5 0

3 years ago

Alex will work on a consulting project for SALT Solutions for 5 days. During these 5 days, the probability that Alex applies for

11Alexandr11 [23.1K]

Answer:

Probability that Alex applies for his first sick leave on the fifth day is 0.0818.

Step-by-step explanation:

We are given that probability that Alex applies for his first sick leave on the second day is 0.21.

The event that Alex applies for sick leave on a particular day is independent of the event that Alex applies for sick leave on other days.

The above situation can be represented through geometric distribution because Geometric distribution probability gives us the probability of 1st success in trial.

<em>Since, here we want our first success in the fifth trial, i.e. Alex applies for his first sick leave on the fifth day.</em>

<em />

<u>The probability distribution for geometric distribution is given by;</u>

$P(X =x) = p \times (1-p)^{x-1} ; x = 1,2,3,4,......$

where, p = probability of success which in our question is Alex applies for his first sick leave = 0.21

x = no. of trials = 5

<em>Let X = Day on which Alex applies for first sick leave</em>

So, X ~ Geo( p = 0.30)

Now, probability that Alex applies for his first sick leave on the fifth day is given by = P(X = 5)

P(X = 5) = $0.21 \times (1-0.21)^{5-1}$

= $0.21 \times 0.79^{4}$

= <u>0.0818</u>

3 0

3 years ago